Computational method and apparatus for predicting polypeptide aggregation or solubility

ABSTRACT

A prediction method for predicting the effect of an amino acid modification on the rate of aggregation (solubility) of a reference polypeptide comprising: calculating the difference in hydrophobicity (ΔHydr) between the reference polypeptide and a modified polypeptide, calculating the difference in β-sheet propensity (ΔΔG coil-α +ΔΔG β-coil ) between the reference polypeptide and modified polypeptide, calculating the difference in charge (ΔCharge) between the reference polypeptide and modified polypeptide, and calculating: [x*ΔHydr]+[y*(ΔΔG coil-α +ΔΔG β-coil )]−[z*ΔCharge], wherein x, y and z are scaling factors.

TECHNICAL FIELD

This invention relates to methods for determining the effect of an aminoacid modification on the rate of aggregation of a polypeptide bycalculating the propensity of a modified polypeptide to aggregate, i.e.the solubility of a modified polypeptide, relative to a referencepolypeptide. The invention further relates to a method for designing amodified polypeptide with a particular ability to aggregate, i.e. aparticular solubility. The invention further relates to such methodscarried out by means of computer software and to computer hardwareprogrammed for carrying out the methods.

BACKGROUND ART

An understanding of the effects of peptide and protein modifications,such as amino acid substitutions, on the propensities of specificpolypeptides to aggregate is of crucial importance for elucidating themolecular basis of protein deposition diseases, such as Alzheimer's andother amyloid diseases, and for understanding the mechanisms of actionof the mutations associated with hereditary forms of such diseases.

In each of the various pathological conditions associated with proteinand peptide deposition, a specific peptide or protein that is normallysoluble is deposited, either intact or in fragmented form, intoinsoluble aggregates that accumulate in one or more type(s) of tissue.Numerous mutations have been found to be associated with familial formsof protein deposition diseases and more than 100 have been showndirectly to involve the sequence of the peptide or protein responsiblefor aggregation (Siepen and Westhead, 2002). Many of these mutationshave been identified over the past 5 years, and the number is expectedto increase dramatically in the near future. Investigation of themechanisms by which natural mutations result in pathological behaviourhas proved to be of fundamental importance for exploring the molecularbasis of the underlying disease, even in those cases where they aresporadic rather than familial in origin (Selkoe, 2001; Volles &Lansbury, 2002).

The ability to form highly organised aggregates having common structuralcharacteristics, such as amyloid, has been found to be a genericproperty of polypeptides, regardless of sequence or structuralsimilarity, and not simply a feature of small numbers of proteinsassociated with recognised pathological conditions (Dobson, 2001).

In the native state, hydrophobic residues are usually embedded withinthe core of a protein, thus the opportunity for these residues tointeract is limited. However, proteins are dynamic and an equilibriumexists between the stable and folded conformation, and destabilised,partially or fully unfolded states. The free energy value (ΔG, kJ mol⁻¹)for a protein provides an indication of the stability of the protein.Aggregation occurs when proteins in their native state denature; as theprotein unfolds, intramolecular bonds are broken, allowing thepolypeptide main chain (backbone) and hydrophobic side chains to beexposed. Hydrogen bonds and other interactions can then form between thepartially or fully denatured protein molecules, resulting inintermolecular associations and aggregate formation.

In some instances, it may be desirable to form aggregates, in particularfibrils, for example for use as plastic materials, in electronics, asconductors, for catalysis or as a slow release form of the polypeptide,or where polypeptide fibrils are to be spun into a polypeptide “yarn”for various applications; for example, as described in published patentapplications WO0017328 (Dobson) and WO0242321 (Dobson & McPhee).

However, in other circumstances the formation of aggregates isdisadvantageous, for example, when it is desired to use a polypeptide atconcentrations or under conditions desirable for physiological activity,therapeutic administration or industrial application. In particular, theuse of bioactive peptides and proteins as pharmaceutical agents islimited where the peptide or protein tends to form aggregates duringmanufacture, processing, storage or following administration. Theseissues are widely recognised in the biotechnological and pharmaceuticalindustry and constitute a major problem and economic burden, that can bedifficult to overcome and may require the use of sophisticatedexpression and refolding techniques, the development of specificformulations, stabilising agents and excipients, cold chain delivery, orimmediate reconstitution before use. Almost all known polypeptidetherapeutic products present these problems, e.g. insulin, interferon-γ,BMPs, calcitonin, glucagon, antibodies.

Various factors are known to affect the tendency of a polypeptide toaggregate. Some of these factors are local to amino acid residues, otherfactors are global and can affect the entire protein. For example, whenmutations are made in a polypeptide, local factors in the region of themutation such as increased hydrophobicity, or tendency to convert fromα-helix to β-sheet conformation, result in a higher rate of aggregationthan that of the wild type (non-mutant) protein. “Global” or overallchanges due to mutations can also affect the rate of aggregation; forexample, a change in net charge of the mutant polypeptide bringing itcloser to neutral results in an increased tendency of a polypeptide toaggregate. Mutations that destabilise the native state of thepolypeptide also result in facilitated aggregation.

A detailed mutational study on a model protein, muscle acylphosphatase(AcP), demonstrated that the rate of aggregation from an ensemble ofpartially denatured conformations can be followed readily for AcP usinga variety of spectroscopic probes. The rate of aggregation wasdetermined for over 50 mutational variants of this protein (Chiti etal., 2002a; 2002b: Chiti, F., Taddei, N., Baroni, F., Capanni, C.,Stefani, M., Ramponi, G. & Dobson, C. M. Kinetic partitioning of proteinfolding and aggregation. Nature Struct. Biol. 9, 137-143 (2002a); Chiti,F., Calamai, M., Taddei, N., Stefani, M. Ramponi, G. & Dobson, C. M.Studies of the aggregation of mutant proteins in vitro provide insightsinto the genetics of amyloid diseases. Proc. Natl. Acad. Sci. USA, 99:16419-16426 (2002b)). Many of these mutations, particularly thoseinvolving residues 16-31 and 87-98, were found to perturb theaggregation rate of AcP very significantly (Chiti et; al., 2002a;2002b). Chiti (2002a) concluded that the measured changes in aggregationrate upon mutation positively correlated with changes in thehydrophobicity and β-sheet propensity of the regions of the protein inwhich the mutations are located. Chiti (2002b) examined AcP mutationsthat altered the charge state of the AcP protein without affectingsignificantly the hydrophobicity or secondary structure propensititiesof the polypeptide chain. An inverse correlation was reported betweenthe rate of aggregation of protein variants under denaturing conditionsand the overall net charge of the protein.

The factors that affect the rate of aggregation of a protein arediverse. When amino acid substitutions are made in a protein, severalfactors are involved to different extents. A single mutation canincrease the net charge, thereby disfavouring aggregation (for example,the replacement of Ala for Asp in a positively charged protein).Nevertheless, the same mutation can increase hydrophobicity, therebybringing an accelerating contribution to the aggregation rate. Finally,the same mutation also changes the α-helical and β-sheet propensities ofthe polypeptide chain, introducing other factors. The relationshipbetween the factors and their relative importance to aggregation(solubility) are not well characterised.

Thus, it has not been possible to predict accurately the tendency of aprotein to form insoluble and ordered aggregates, such as amyloidfibrils, nor to predict or calculate the effect of specific amino acidmodifications, such as replacements, on aggregation/solubility. Theinability to make such predictions or calculations constitutes a problemin the design and/or handling of polypeptides, whether in vivo or invitro.

The ability to predict the intrinsic effects of mutations on polypeptideaggregation is of crucial importance in elucidating the pathogeniceffect of the large numbers of mutations associated with proteindeposition diseases. It would be desirable to establish, in specificcases, whether a given mutation would give rise to the disease as adirect result of its effect on the aggregation process of thepolypeptide involved, or by other mechanisms. In addition, theestablishment of general principles in aggregation would make itpossible to use statistical methods to analyse the relationships betweenmutation, aggregation and disease. An understanding of the effects ofamino acid substitutions on the propensities of specific proteins toaggregate would allow the establishment of criteria to modify rationallythe aggregational properties of natural or designed peptides andproteins for industrial processes, research purposes, medical treatmentor biotechnological application. Furthermore, methods of the inventionmay be used to identify or design polypeptide sequences with a reducedaggregation propensity, re-designed polypeptides could be administeredby methods such as gene therapy to treat certain disorders, particularlythose associated with protein aggregation. The ability to identify ordesign polypeptides with specific aggregation properties will beimportant for development and manufacture of polypeptides forapplications in the material and device areas, such as those describedin WO0017328 (Dobson) and WO0242321 (Dobson & McPhee).

It would therefore be useful to be able to predict if a particularpolypeptide would form insoluble aggregates and to predict the effectthat a particular modification or modifications of amino acid sequencewould have on the aggregation/solubility properties of a polypeptide.

DISCLOSURE OF INVENTION

The invention provides a prediction method for predicting the effect ofan amino acid modification on the rate of aggregation (solubility) of areference polypeptide, which method comprises calculating the differencein hydrophobicity (ΔHydr) between the reference polypeptide and amodified polypeptide, calculating the difference in β-sheet propensity(ΔΔG_(coil-α)+ΔΔG_(β-coil)) between the reference polypeptide andmodified polypeptide, calculating the difference in charge (ΔCharge)between the reference polypeptide and modified polypeptide andcalculating: [x*ΔHydr]+[y*(ΔΔG_(coil-α)+ΔΔG_(β-coil))]−[z*ΔCharge],wherein x, y and z are scaling factors. A value for[x*ΔHydr]+[y*(ΔΔG_(coil-α)+ΔΔG_(β-coil))]−[z*ΔCharge] of a first signindicates that the modified polypeptide has a greater propensity toaggregate relative to the reference polypeptide and a value for[x*ΔHydr]+[y*(ΔΔG_(coil-α)+ΔΔG_(β-coil))]−[z*ΔCharge] of a sign oppositeto the first sign indicates that the modified polypeptide has a reducedpropensity to aggregate relative to the reference polypeptide. If theeffect of the amino acid modification on the rate of aggregation isexpressed as ln(ν_(mod)/ν_(ref)), a positive value forln(ν_(mod)/ν_(ref)), indicates that the modified polypeptide has agreater propensity to aggregate (lower solubility) relative to thereference polypeptide; and a negative value for ln(ν_(mod)/ν_(ref)),indicates that the modified polypeptide has a reduced propensity toaggregate (higher solubility) relative to the reference polypeptide.

In a preferred method the scaling factor x is a value from 0.59 to 0.64to, the scaling factor y is a value from 0.19 to 0.22 and the scalingfactor z is a value from 0.49 to 0.51. It is particularly preferred thatthe scaling factor x is 0.6, 0.63 or 0.633, the scaling factor y is 0.2or 0.198 and the scaling factor z is 0.5, 0.49 or 0.491.

The invention also provides an identification method for identifying anamino acid modification that reduces the aggregation rate (increases thesolubility) of a reference polypeptide comprising using a method of theinvention to predict the change in aggregation rate for one or moremodified polypeptide(s), the modified polypeptide having one or moreamino acid modification(s) when compared to the reference polypeptide,comparing the predicted-aggregation rates of the reference and said oneor more modified polypeptides, and identifying one or more modifiedpolypeptide(s) having a predicted reduced aggregation rate relative tothe reference polypeptide. In another aspect, the present inventionprovides a modified polypeptide having a reduced aggregation rateidentified by this method. The invention further provides a predictionmethod as hereinbefore described for use in the identification method orin the preparation of a modified polypeptide

The invention also provides an identification method for identifying anamino acid modification that increases the aggregation rate (decreasesthe solubility) of a polypeptide comprising using a method of theinvention to predict the change in aggregation rate for one or moremodified polypeptide(s), each modified polypeptide having one or moreamino acid modification(s) when compared to the reference polypeptide,comparing the predicted aggregation rates of the reference and said oneor more modified polypeptide(s) and identifying one or more modifiedpolypeptides having a predicted increased aggregation rate relative tothe reference polypeptide. Additionally, the present invention providesa modified polypeptide having an increased aggregation rate identifiedby this method.

A method is provided for making a polypeptide having a reducedaggregation rate (increased solubility) comprising using a method of theinvention to identify a modification predicted to reduce the aggregationrate of a polypeptide and making a modified polypeptide having saidmodification. Also provided is a modified polypeptide having a reducedaggregation rate obtained by this method.

A method is provided for making a polypeptide having an increasedaggregation rate (decreased solubility) comprising using a method of theinvention to identify a modification predicted to increase theaggregation rate of a polypeptide and making a modified polypeptidehaving said modification. Another aspect of the invention provides amodified polypeptide having an increased aggregation rate obtained bythis method.

In an aspect of the invention the reference and modified polypeptide(s)are structurally related in terms of amino acid composition andsequence. Structurally related polypeptides have at least 60%,preferably at least 70%, more preferably at least 80%, yet morepreferably at least 90%, further preferably at least 95% amino acidsequence homology. In an alternative aspect, the reference and modifiedpolypeptide(s) are structurally unrelated. Preferably the referencepolypeptide is a wild type polypeptide and the modified polypeptide is amutant thereof. A modified polypeptide is preparable by chemicalmodification and/or by modification(s) such as substitution, deletionand/or addition of one or more amino acids of the reference protein. Anamino acid substituted or added to the reference protein may be anatural amino acid or a chemically synthesised or chemically modifiedamino acid. Preferably 1 to 20, 1 to 16, 1 to 12, or 1 to 10 amino acidsare substituted, deleted and/or added; most preferably 1, 2, 3, 4, 5, or6 amino acids are substituted, deleted and/or added. Preferably, themodification of the polypeptide is by amino acid substitution, which canbe substitution of one or more amino acids, preferably by substitutionof 1 to 20, 1 to 16, 1 to 12, or 1 to 10 amino acids, more preferablysubstitution of 1, 2, 3, 4, 5, or 6 amino acids. Alternatively,modification the polypeptide may be by deletion of one or more aminoacids, preferably by deletion of 1 to 20, 1 to 16, 1 to 12, or 1 to 10amino acids; more preferably by deletion of 1, 2, 3, 4, 5, or 6 aminoacids.

The reference polypeptide may be a natural polypeptide from any species,or a non-natural “designed” polypeptide. Proposed modifications of thereference polypeptide may be selected by comparing the amino acidsequence of a reference polypeptide with the amino acid sequence of arelated polypeptide or polypeptides from different species. It ispreferred that modification be made in regions of a polypeptide that arepolymorphic between different species. Proposed modifications of areference protein may also be selected by comparing the amino acidsequence of the reference protein with naturally occurring or inducedpolypeptide variants of the reference protein, preferably by comparingwild type and mutant polypeptides.

The reference polypeptide is preferably a human polypeptide. Proposedmodifications of a human reference polypeptide may be selected bycomparing a human reference polypeptide with a related polypeptide froma non-human source. Modification may be such that an amino acid in thehuman form of a polypeptide is modified to the amino acid present atthat position in a related polypeptide from a non-human source.Alternatively, the reference polypeptide may be a non-human polypeptideand the modification may be such that the non-human polypeptide is“humanised”.

For bioactive polypeptides, it is preferred that modification is suchthat an activity of the polypeptide is maintained or improved. Themodification may be outside the active site of the polypeptide or may bewithin the active site of the polypeptide.

The term polypeptide as used herein encompasses proteins and peptides.

Using the methods of the invention, the intrinsic effects of specificmodifications, such as mutations, on the rates of aggregation ofpolypeptides can be rationalised and predicted to a remarkable extent onthe basis of simple physical principles: the effects that themodifications have on the fundamental parameters of hydrophobicity andsecondary structure propensity at the site of modification, and oncharge of the molecule as a whole. Based on this calculation, modified(e.g. mutant) polypeptides can be designed that are more/less liable toaggregate (that have a lesser or greater solubility) than the reference(e.g. wild type) polypeptide, or that have a propensity to aggregatewithin a desired range. Thus it is possible to assess the effects thatvarious amino acid modifications will have on the properties of apolypeptide without having to make modified polypeptides and measureexperimentally the effect of the changes. Design of massive numbers ofmodified polypeptides is feasible, even for a relatively short referencepolypeptide. This is important because modifications can be selectedalso to fulfil other criteria or restrictions, such as proteinstability, function etc.

The change of aggregation rate as a result of a modification (e.g.mutation) can be expressed as ln(ν_(mod)/ν_(ref)), e.g.(ln(ν_(mut)/ν_(wt))). The rate of aggregation may also be expressed interms of an aggregation time, such as a half time of aggregation, and aratio of aggregation rate is equivalent to a ratio of aggregation times,as discussed further later.

The kinetic parameters for aggregation can be aggregation ratescorresponding to an exponential kinetic of aggregation (ν) or, when atime parameter (τ) is used,(τ_(mod)/τ_(ref))=(ν_(ref)/ν_(mod))=1/exp(ln(ν_(mod)/ν_(ref))), caninclude or refer exclusively to nucleation stages and/or “lag phases” ofthe aggregation kinetics (T1) or to the half-time of aggregation of theoverall process (T2).

Change of hydrophobicity (ΔHydr) is calculated usingΔHydr=Hydr_(ref)−Hydr_(mod), where ΔHydr is the change of hydrophobicitythat would result from a proposed amino acid modification, Hydr_(ref)and Hydr_(mod) are the hydrophobicity values of the reference andmodified amino acid residues, respectively.

A consensus hydrophobicity scale can be used to assign a hydrophobicityvalue for each amino acid. Different hydrophobicity scales may be usedfor different pH values, for example, scales described in Cowan, R. &Whittaker, R. G. (1990) Peptide Research 3: 75-80) may be used tocalculate the hydrophobicity of polypeptides at low pH. An averagedhydrophobicity scale can be used, which can be obtained by using acombination of scales, such as those available in the literature (e.g.Fauchere J.-L & Pliska V. E. (1983) Eur. J. Med. Chem. 18: 369-375; KyteJ., Doolittle R. F. (1982) J. Mol. Biol. 157: 105-132). In a preferredembodiment, the hydrophobicity value for each amino acid is assignedusing the values given in Table 1 for hydrophobicity of the 20 aminoacid residues at neutral pH based on the partition coefficients fromwater to octanol; the data are from column 6 of Table 4.8 in Creighton(1993) (Creighton, T. E. In Proteins. Structure and molecularproperties. Second edition. W. H. Freeman & Company (New York, 1993), p.154).

The scaling factor x can be derived by plotting observedln(ν_(mod)/ν_(ref)), e.g. ln(ν_(mut)/ν_(wt)), versus ΔHydr for a numberof polypeptide sequences, which may be unrelated or related (e.g. acollection of AcP mutants) and determining the line of best fit, thescaling factor x the slope (gradient) of the line.

To calculate propensity to convert from α-helical to β-sheet structure(ΔΔG_(coil-α)+ΔΔG_(β-coil)), the individual values for ΔΔG_(coil-α) andΔΔG_(β-coil) are calculated.

ΔΔG_(coil-α) can be calculated using: ΔΔG_(coil-α)=RT ln(P_(α)^(ref)/P_(α) ^(mod)), where ΔΔG_(coil-α) is the predicted change of freeenergy for the transition from α-helix to random coil resulting frommodification; R=0.008314 kJ mol⁻¹K⁻¹, P_(α) ^(ref) and P_(α) ^(mod) arerespectively the predicted α-helical propensities (helix percentages) ofthe reference (e.g. wild type) and modified (e.g. mutant) sequences atthe site of amino acid modification, respectively. The predictedα-helical propensities can be calculated using modellingsoftware/algorithms such as AGADIR(www.embl-heidelberg.de/Services/serrano/agadir/agadir-start.html) Muñoz& Serrano (1994) Nature Structural Biol 1, 399-409; Muñoz & Serrano(1994) J Mol Biol 245, 297-308; Muñoz & Serrano (1997) Biopolymers 41495 509 and Lacroix et al (1998) J Mol Biol 284 173-191; PED (Rost, B.et al, (1993) J Mol Biol 232, 584-599); PROF (Rost, B. et al, (1996)Methods Enzymol 266, 525-539); GOR4 (Garnier J et al (1978) J Mol Biol120, 97-120; Garnier J et al (1996) Methods Enzymol 266, 540-553). Anysuitable algorithms based on structural databases, structural preferencedatabases or rotamer preference databases could be used for thiscalculation to estimate helical propensities, for example, GOR IV: J.Garnier, J. F. Gibrat and B. Robson in Methods Enzymol., vol 266, p540-553 (1996). J. Garnier, D. Osguthorpe and B. Robson (J. Mol. Biol.120, 97, 1978). J Mol Biol 1987 Dec. 5; 198(3):425-443 (GOR-III); PHD:Rost B, Sander C. J Mol Biol 1993 Jul. 20; 232(2):584-99. Rost B, SanderC. Proteins 1994 May; 19(1):55-72; PREDATOR Frishman D, Argos P. ProteinEng 1996 February; 9(2):133-142; SIMPA/SIMPA96: Levin J M, Robson B,Garnier J. FEBS Lett 1986 Sep. 15; 205(2):303-308. J. LEVIN, J. GARNIER.Biochim. Biophys. Acta, (1988) 955, 283-295. Levin J M. Protein Eng.(1997), 7, 771-776. SOPM/SOPMA Geourjon C, Deleage G. Protein Eng 1994February; 7(2):157-164. Geourjon C, Deleage G. Comput Appl Biosci 1995December; 11(6):681-684.

ΔΔG_(β-coil) can be calculated using: ΔΔG_(β-coil)=13.64 (P_(β)^(ref)−P_(β) ^(mod)), where ΔΔG_(β-coil) is the change of free energyfor the transition from random coil to β-sheet resulting from themodification (ΔG_(β-coil)), 13.64 is the conversion constant from thenormalised scale to units of kJ mol⁻¹; P_(β) ^(ref) and P_(β) ^(mod) arethe normalised β-sheet propensities of the reference (e.g. wild type)and modified (e.g. mutant) residue, respectively. Values of β-sheetpropensity for all 20 amino acids can be determined using a publishedscale. A preferred scale is given in Table 1, which provides β-sheetpropensity values for 19 amino acid residues (all except proline), theseare normalised from 0 (high β-sheet propensity) to 1 (low β-sheetpropensity). These data are from column 4 of Table 1 of Street and Mayo(1999) (Street, A. G. & Mayo, S. L. Intrinsic β-sheet propensitiesresult from van der Waals interactions between side chains and the localbackbone. Proc. Natl. Acad. Sci. USA, 96, 9074-9076 (1999)). The β-sheetpropensity of proline is not reported due to the difficulty indetermining it experimentally. The β-sheet propensity of glycine isobtained from theoretical calculations.

The scaling factor y can be derived by plotting observedln(ν_(mod)/ν_(ref)) versus (ΔΔG_(coil-α)+ΔΔG_(β-coil)) for a number ofunrelated or related polypeptide sequences (e.g. by plotting observedln(ν_(mut)/ν_(wt)) versus (ΔΔG_(coil-α)+ΔΔG_(β-coil)) for a number ofAcP polypeptide mutations) and determining the line of best fit, thescaling factor y is the slope (gradient) of the line.

Change of charge (ΔCharge) of the polypeptide is calculated using:

ΔCharge=|Charge_(mod)|−|Charge_(ref)|, where ΔCharge is the change ofcharge resulting from the mutation, |Charge_(mod)| and |Charge_(ref)|are the absolute values of charge for the modified (e.g. mutant) andreference (e.g. wild-type) sequences, respectively (obtained from thesums of the charge values for amino acid residues (e.g. the values givenin Table 1, which are at neutral pH). The operator of “absolute value”is introduced so that a negative value of ΔCharge results from theequation when the mutation causes the entire protein or peptide toapproach neutrality, regardless of the initial sign of the proteinsequence. A positive value of ΔCharge is obtained when the mutationcauses the entire protein sequence to deviate further from neutrality.

The scaling factor z can be derived by plotting observedln(ν_(mod)/ν_(ref)) versus ΔCharge for a number of related or unrelatedpolypeptide sequences, e.g. by plotting observed ln(ν_(mut)/ν_(wt)) fora number of AcP polypeptide mutants, and determining the line of bestfit; the scaling factor z is the slope (gradient) of the line.

The scaling factors x, y, and z can be refined by plotting a largernumber of data points for further polypeptide modifications. A multipleregression analysis can be used to determine the scaling factors x forΔHydr, y for ΔΔG_(coil-α)+ΔΔG_(β-coil), and z for ΔCharge. The multipleregression analysis method consists of calculating simultaneously theindividual scaling factors x, y, and z for a given set of polypeptides(e.g. mutant polypeptides) for which the experimental values ofln(ν_(mod)/ν_(ref)) (e.g. ln(ν_(mut)/ν_(wt))) are available. Initialestimations for the values of x, y and z, such as the values describedherein or values chosen on an arbitrary basis, can be used in thecalculations. The calculated ln(ν_(mod)/ν_(ref)) values are comparedwith the values obtained experimentally. The calculations can berepeated through a number of iterations, each time using a differentcombination of x, y, and z values. The iterations will end when a set ofbest values is found for x, y and z, i.e. when minimal differencebetween the calculated and experimental value of ln(ν_(mod)/ν_(ref)) isfound.

The calculation can be modified by inclusion of another term or terms,such as a stability factor to correct for mutations that affect proteinstability. Terms can be added to the equation to represent other factorsthat affect aggregation rate, such as the position of the mutation alongthe sequence, non-cumulative effects of double substitutions, distancein sequence between double substitutions. Refinement of the equation byinclusion of additional factors can improve the accuracy of the method.Accordingly, methods of the invention can further comprise an additionalcalculation step or steps, for example, an additional step in which astability factor is used to correct for mutations that affect proteinstability.

The invention also provides computer program code to, when running,predict the effect of an amino acid modification on the rate ofaggregation of a polypeptide, the code comprising code to: input anamino acid modification that would convert the reference polypeptide toa modified form of the polypeptide; calculate a difference inhydrophobicity (ΔHydr) between the reference polypeptide and modifiedpolypeptide; calculate a difference in β-sheet propensity(ΔΔG_(coil-α)+ΔΔG_(β-coil)) between the reference polypeptide andmodified polypeptide; calculate a difference in charge (ΔCharge) betweenthe reference polypeptide and modified polypeptide; and calculate:[x*ΔHydr]+[y*(ΔΔG_(coil-α)+ΔΔG_(β-coil))]−[z*ΔCharge], wherein x, y andz are scaling factors.

We also describe computer program code to, when running, identify apolypeptide, the code comprising: code to predict the change inaggregation rate for one or more modified polypeptides, comprising codeas described above; and further code to identify one or more of saidmodified polypeptides dependent upon said predicted change inaggregation rate.

The invention also provides a computer system for determining a rate ofaggregation of a second polypeptide in relation to a referencepolypeptide, said second polypeptide and said reference polypeptide eachhaving an amino acid sequence, the amino acid sequence of said secondpolypeptide comprising a modified version of the amino acid sequence ofsaid reference polypeptide, the computer system comprising a data storefor storing data comprising hydrophobicity data, β-sheet propensity dataand charge data for a set of amino acids; a program store storingprocessor implementable code; and a processor, coupled to said programstore and to said data store for implementing said stored code, the codecomprising code for controlling the processor to: input an amino acidsequence for said second polypeptide; read hydrophobicity data for saidsecond polypeptide amino acid sequence from said data store anddetermine a hydrophobicity value for said second polypeptide; readchange data for said second polypeptide amino acid sequence from saiddata store and determine a β-sheet propensity value for said secondpolypeptide; determine an α-helix propensity value for said secondpolypeptide; obtain hydrophobicity data, charge data, β-sheet propensitydata and an α-helix propensity value for said reference polypeptide; anddetermine said relative rate of aggregation using said hydrophobicity,change, β-sheet and α-helix propensity data for said second andreference polypeptide. The terms “second polypeptide” and “modifiedpolypeptide” are used interchangeably.

In an embodiment the β-sheet propensity may be expressed in terms offree energy. The set of amino acids may comprise, for example, all thenatural amino acid residues. The α-helix propensities of the referenceand modified polypeptide sequences may be determined using a code withinthe computer system or a request may be sent to a separate computersystem, for example on a network, and α-helix propensity data receivedback from this second computer system. The hydrophobicity data, chargedata and secondary structural propensity data for the reference andmodified polypeptides may be determined from scales of values for eachamino acid that were previously published and input to the computersystem and/or stored, for example in the data store. The relative rateof aggregation determined by the apparatus may simply comprise adetermination of whether the aggregation rates (or in other embodiments,the solubility) of the second polypeptide is above or below that of thereference polypeptide; alternatively a quantitative determination of therelative aggregation rates of these polypeptides may be made. Preferablythe code evaluates the sum of a difference in hydrophobicity, adifference in secondary structural propensity and a difference in chargebetween the second polypeptide and the reference polypeptide, eachmultiplied by a scaling factor. One or more of the scaling factors maybe selected responsive to, for example, the type of polypeptide forwhich the determination is being made.

The computer system may be used to evaluate a plurality of secondpolypeptides, presenting the results, for example, as an ordered list orgraph and/or selecting a promising candidate sequence for synthesis andfurther evaluation.

In a further aspect the invention provides a method of determining arelative aggregation rate indicator, said relative aggregation rateindicator predicting a rate of aggregation of a second polypeptide incomparison to a rate of aggregation of a reference polypeptide, saidsecond polypeptide comprising a version of said reference polypeptidewith a modified amino acid sequence, the method comprising: determininga difference in hydrophobicity between said second polypeptide and saidreference polypeptide; determining a difference in a secondary structurepropensity between said second polypeptide and said referencepolypeptide; determining a difference in charge between said secondpolypeptide and said reference polypeptide; forming a weightedcombination of said difference in hydrophobicity, said difference insecondary propensity of said difference in change to determine saidrelative aggregation rate indicator.

The invention further provides computer programme code to implement theabove-described methods, and computer apparatus programmed to implementthe methods. Embodiments of the methods may be implemented usingcomputer programme code in peptide synthesis apparatus, preferablyapparatus for automatically synthesising a polypeptide based uponresults obtained by applying the methods. The invention also encompassespolypeptides synthesised in this manner.

The program code may be provided on a data carrier or storage medium,such as a hard or floppy disk, ROM or CD-ROM, or on an optical orelectrical signal carrier, for example via a communications network. Theprocessor control code may comprise program code in any conventionalprogramming language for example C or assembler or machine code, andembodiments of the invention may be implemented on a general purposecomputer system.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows the change of the aggregation rate of AcP resulting frommutation plotted against (a) the predicted change of hydrophobicity, (b)propensity to convert from an α-helical to a β-sheet conformation and(c) charge.

FIG. 2( a) shows the calculated versus observed change of theaggregation rate upon mutation for the short peptides or nativelyunfolded proteins listed in Table 2.

FIG. 2( b) shows the calculated versus observed change of theaggregation rate upon mutation for 27 amino acid substitutions of AcPwithin two regions of the sequence that appear to be relevant foraggregation and encompassing residues 16-31 and 87-98.

FIG. 3 shows a block diagram of a computer system for implementing anaggregation rate determination procedure according to an embodiment ofan aspect of the present invention.

FIG. 4 shows a flow diagram of a comparative aggregation ratedetermination procedure according to an embodiment of the presentinvention.

FIG. 5 shows a flow diagram of an automated protein synthesis candidatedetermination procedure.

EXAMPLES Example 1 AcP Experimental Work

The rates of aggregation for wild type AcP protein (ν_(wt)) and forvarious AcP mutants (variants) (ν_(mut)) were measured upon denaturationin 25% TFE, from time courses of ThT fluorescence, as described by Chitiet al., 2002a (Chiti, P., Taddei, N., Baroni, F., Capanni, C., Stefani,M., Ramponi, G. & Dobson, C. M. Kinetic partitioning of protein foldingand aggregation. Nature Struct. Biol. 9, 137-143 (2002a)). Allaggregation rate measurements were carried out under conditions in whichall protein variants consist of ensembles of relatively unstructuredconformations. The change of aggregation rate as a result of a mutationwas expressed in all cases as the natural logarithm of the ratio of theaggregation rate constants of the mutant and wild-type protein(ln(ν_(mut)/ν_(wt))).

In Table 1, the hydrophobicity values of the 20 amino acid residues atneutral pH are based on the partition coefficients from water tooctanol. These data are from column 6 of Table 4.8 in Creighton (1993)(Creighton, T. B. In Proteins. Structure and molecular properties.Second edition. W. H. Freeman & Company (New York, 1993), p. 154)). Theβ-sheet propensities of the 20 amino acid residues are normalised from 0(high β-sheet propensity) to 1 (low β-sheet propensity). These data arefrom column 1 of Table 4 of Street and Mayo (1999) (Street, A. G. &Mayo, S. L. Intrinsic β-sheet propensities result from van der Waalsinteractions between side chains and the local backbone. Proc. Natl.Acad. Sci. USA, 96, 9074-9076 (1999)). The β-sheet propensity of prolineis not reported due to the difficulty in determining it experimentally.The β-sheet propensity of glycine is obtained from theoreticalcalculations. The values of charge are at neutral pH. Values in bracketsare at a pH lower than 6.0, when the histidine residue is positivelycharged.

TABLE 1 Scales of hydrophobicity, β-sheet propensity and charge for the20 natural amino acids amino acid residue hydrophobicity (kJ mol⁻¹)β-sheet propensity charge Arg (R) 3.95 0.35 +1 Lys (K) 2.77 0.34 +1 Asp(D) 3.81 0.72 −1 Glu (E) 2.91 0.35 −1 Asn (N) 1.91 0.40 0 Gln (Q) 1.300.34 0 His (H) 0.64 (2.87) 0.37 0 (+1) Ser (S) 1.24 0.30 0 Thr (T) 1.000.06 0 Tyr (Y) −1.47 0.11 0 Gly (G) 0.00 0.60 0 Pro (P) −0.99 n.d. 0 Cys(C) −0.25 0.25 0 Ala (A) −0.39 0.47 0 Trp (W) −2.13 0.24 0 Met (M) −0.960.26 0 Phe (F) −2.27 0.13 0 Val (V) −1.30 0.13 0 Ile (I) −1.82 0.10 0Leu (L) −1.82 0.32 0

Using the data in Table 1, the change of hydrophobicity (ΔHydr),propensity to convert from α-helical to β-sheet structure(ΔΔG_(coil-α)+ΔΔG_(β-coil)) and change of charge (ΔCharge) werequantified for AcP using the tabulated values for all the amino acidresidues.

The change in hydrophobicity (ΔHydr) resulting from mutation wascalculated using ΔHydr=Hydr_(wt)−Hydr_(mut), where Hydr_(wt) andHydr_(mut) are the hydrophobicity values of the wild type and mutantresidues, respectively (the values of hydrophobicity for all 20 aminoacids are listed in Table 1).

To calculate the propensity to convert from α-helical to β-sheetstructure (ΔΔG_(coil-α)+ΔΔG_(β-coil)), it was necessary to calculateΔΔG_(coil-α) and ΔΔG_(β-coil).

The change of free energy for the transition random coil→β-sheetresulting from mutation (ΔΔG_(β-coil)) was calculated usingΔΔG_(β-coil)=13.64 (P_(β) ^(wt)−P_(β) ^(mut)). P_(β) ^(wt) and P_(β)^(mut) are the normalised β-sheet propensities of the wild-type andmutant residue, respectively (the values of β-sheet propensity for all20 amino acids are listed in Table 1), and 13.64 is the conversionconstant from the normalised scale to units of kJ mol⁻¹.

The predicted change of free energy for the transition α-helix→randomcoil resulting from mutation (ΔΔG_(coil-α)) was calculated usingΔΔG_(coil-α)=RT ln(P_(α) ^(wt)/P_(α) ^(mut)). P_(α) ^(wt) and P_(α)^(mut) are the predicted α-helical propensities (helix percentages) ofthe wild type and mutated sequences at the site of mutation,respectively which were calculated using the AGADIR algorithm atwww.embl-heidelberg.de/Services/serrano/agadir/agadir-start.html);R=0.008314 kJ mol⁻¹K⁻¹. (see also Lacroix, E., Viguera A R & Serrano, L.(1998). J. Mol. Biol. 284, 173-191).

The change of charge resulting from the mutation (ΔCharge) wascalculated using ΔCharge=|Charge_(mut)|−|Charge_(wt)|, where|Charge_(wt)| and |Charge_(mut)| are the absolute values of charge forthe wild-type and mutated sequences, respectively (obtained from thesums of the charge values of all residues reported in Table 1).

The change of aggregation rate upon mutation ln(ν_(mut)/ν_(wt)) wasplotted individually against ΔHydr, against (ΔΔG_(coil-α)+ΔΔG_(β-coil))and against ΔCharge, these plots are shown in FIGS. 1 a, 1 b and 1 c,respectively.

The mutations reported in FIGS. 1 a and 1 b, described previously (Chitiet al., 2002a, ibid.), do not involve change of charge. The mutationsreported in FIG. 1 c, described previously (Chiti et al., 2002b, ibid.),were designed to minimise change of hydrophobicity and secondarystructure propensities. Most of the amino acid substitutions of AcPinvolve residues within the two regions of the sequence, encompassingresidues 16-31 and 87-98, that are thought to be relevant foraggregation.

The solid lines through the data represent the best fits to linearfunctions. The r and p values resulting from each correlation and theslope of the best fits are shown in each case.

In each of the analyses, the data points are considerably scatteredaround the lines representing the best fits to linear functions. Thisscatter can be attributed to the fact that only a single parameter isconsidered in each case, to the difficulty in predicting accuratelychanges in the hydrophobicity and secondary structure propensities, andto the varying relative importances of the different sites of mutationin the aggregation process. Despite the scatter present in each plot,however, the change of aggregation rate upon mutation(ln(ν_(mut)/ν_(wt))) for AcP was found to correlate significantly witheach of these parameters individually FIGS. 1 a, 1 b, and 1 c). TheDespite the scatter present in each plot, however, the change ofaggregation rate upon mutation (ln(ν_(mut)/ν_(wt))) for AcP was found tocorrelate significantly with each of these parameters individually FIGS.1 a, 1 b, and 1 c). Average dependency of ln(ν_(mut)/ν_(wt)) on eachparameter was calculated (the slope of the line of best fit resultingfrom each analysis. The values were found to be:

ΔHydr 0.633 ΔΔG_(coil-α) + ΔΔG_(β-coil) 0.198 ΔCharge 0.491

Following this analysis, Equation 1 was devised and used to determinethe change of aggregation rate upon mutation (ln(ν_(mut)/ν_(wt)) value):

ln(ν_(mut)/ν_(wt))=0.633*ΔHydr+0.198*(ΔΔG _(coil-α) +ΔΔG_(β-coil))−0.491*ΔCharge

where the numbers preceding the parameters of ΔHydr,(ΔΔG_(coil-α)+−ΔΔG_(β-coil)) and ΔCharge are values for x, y and zrespectively that correspond to the slopes of the three plots reportedin FIG. 1 (i.e. the dependencies of ln(ν_(mut)/ν_(wt)) on the threeparameters).

Example 2 Comparison of Observed Versus Calculated Change in AggregationRate on Mutation of AcP Protein/Relative Aggregation Rates of Mutant AcPProteins

Using Equation 1, the change of aggregation rate ln(ν_(mut)/ν_(wt)) wascalculated for 27 amino acid substitutions of AcP within the two regionsof the sequence that appear to be relevant for aggregation andencompassing residues 16-31 and 87-98. The change of aggregation ratefor each mutation was determined experimentally, as described in Example1, under conditions in which all protein variants consist of ensemblesof relatively unstructured conformations. The calculated versus theexperimental values of ln(ν_(mut)/ν_(wt)) for all the mutations of AcPwere plotted as shown in FIG. 2 b. The observed correlation was found tobe highly significant (r=0.756 and p<0.0001) and the slope was close to1.

Example 3 Comparison of Observed Versus Calculated Change in Rate ofAggregation on Mutation for a Range of Polypeptides

The combined function, Equation 1, was applied to calculate the changein aggregation rate upon mutation (calculated ln(ν_(mut)/ν_(wt))) for 26mutations in the polypeptides amylin, prion peptides, α-synuclein,amyloid β-peptide, tau, leucine rich repeat and a model peptide, aslisted in Table 2.

Values for ΔHydr, ΔΔG_(coil-α)+ΔΔG_(β-coil) and ΔCharge were calculatedfor each polypeptide mutation using the methods described in Example 1.

The 26 mutations considered included both physiologically relevantmutations associated with genetic forms of protein deposition diseasesand other substitutions that had been used in research to addressspecific issues. They were all mutations of either unstructured proteins(peptides), or polypeptides that appear to be natively unfolded, such asthe amyloid β peptide, the islet amyloid polypeptide, α-synuclein, tau,short peptides dissected from the sequence of the prion protein andother model peptides. Only single-point mutations within shortunstructured peptides or proteins that are unfolded under conditionsclose to physiological were considered in the analysis. All mutationswere included for which actual experimental values of ln(ν_(mut)/ν_(wt))were directly available or could be determined from data in theliterature. Mutations that acted simply by destabilising the nativestate of the protein involved were excluded. Data were consideredregardless of the experimental techniques employed by the differentauthors to probe aggregation, provided a quantitative analysis could becarried out. When time or rate constants were not explicitly reported,the plots describing the kinetic profiles of aggregation were scannedand computer-analysed. This procedure allowed plots with numericalvalues of the data points to be reconstructed and analysed to obtainrate constant values. When lag and growth phases were evident in thekinetic profiles of aggregation, only the growth phase was considered.When data at fixed periods of time were reported (for example by meansof bar graphs), the value for observed ln(ν_(mut)/ν_(wt)) value wasobtained from the ratio of the aggregation parameters of the mutated andwild-type protein (peptide), before equilibrium was reached.

Mutations involving proline residues were not analysed because of thedifficulty in obtaining quantitative estimates of the change of β-sheetpropensity as a result of these mutations (see Table 1). Nor weremutations considered when substantial discrepancies in theln(ν_(mut)/ν_(wt)) value were reported by different authors (whensignificant but not substantial discrepancies were present, weconsidered ln(ν_(mut)/ν_(wt)) values resulting from averages of theavailable data).

TABLE 2 Changes of hydrophobicity, secondary structure propensities,charge and aggregation rate as a result of single-point mutations ofunstructured peptides or natively unfolded proteins. calculated observedΔHydr ΔΔG_(β-coil) ΔΔG_(coil-α) ln(ν_(mut)/ ln (ν_(mut)/ Mutation (kJmol⁻¹) (kJ mol⁻¹) (kJ mol⁻¹) ΔCharge ν_(wt)) ν_(wt)) ref. amylin N22A2.30 −0.95 −3.36 0 0.60 0.69 11 F23A −1.88 −4.64 −3.90 0 −2.88 −2.65 11G24A 0.39 1.77 −2.84 0 0.04 −0.03 11 I26A −1.43 −5.05 −0.32 0 −1.97−2.39 11 L27A −1.43 −2.05 0.36 0 −1.24 −0.93 11 S20G 1.24 −4.09 0.00 0−0.03 1.01 12 prion peptides H111A 3.26 −1.36 −3.21 −1 1.65 0.60 13H111K 0.10 0.41 −1.72 0 −0.20 −0.26 13 A117V 0.91 4.63 2.37 0 1.96 1.5113 V210I 0.52 0.41 −0.97 0 0.22 0.84 14 α-synuclein A53T −1.39 5.59 2.830 0.79 1.18 15 A76E −3.30 1.64 0.00 1 −2.25 −2.72 16 A76R −4.34 1.640.64 −1 −1.80 −0.93 16 Amyloid-β peptide A21G −0.39 −1.77 3.27 0 0.05−0.07 17 E22K 0.14 0.14 −1.72 −2 0.76 0.92 18 E22Q 1.61 0.14 0.00 −11.54 2.92 17, 18 E22G 2.91 −3.41 4.30 −1 2.51 2.03 19 D23N 1.90 4.36−1.72 −1 2.22 3.97 17 F19T −3.27 0.95 −1.76 0 −2.23 −2.48 20 Tau G272V1.30 6.41 −1.71 0 1.75 1.04 21, 22 R406W 6.08 1.50 0.00 −1 4.64 1.25 21,22, 23 Y310W 0.66 −1.77 000 0 0.07 0.05 23bis Leucine-rich repeat D24N1.90 4.36 −3.43 −1 1.88 2.08 24 D24Q 2.51 5.18 −3.10 −1 2.49 1.25 24Model peptide D6E 0.90 5.04 −2.27 0 1.12 0.40 25 D6N 1.90 4.36 0.00 11.57 0.52 25

The calculated versus the experimental value of ln(ν_(mut)/ν_(wt)) wasplotted and is shown in FIG. 2( a). The highly significant correlation(r=0.84, p<0.0001), and the value of the slope that is close to 1.0,indicate close agreement between calculated and experimental effects ofmutations on the aggregation rates of this heterogeneous group ofpolypeptides. The observed changes of aggregation rate upon mutationspan a range of ca. 800 times, i.e. from 15 slower to 53 faster than thecorresponding wild-type polypeptide (FIG. 2 a and Table 2). 84% of thesemutations have calculated values of ln(ν_(mut)/ν_(wt)) that vary withina factor of 3 from the observed values of ln(ν_(mut)/ν_(wt)). Thepercentage rises to 92% and 96% if spread factors of 5 and 10 areconsidered, respectively. Examples where close agreement is foundbetween theoretical and experimental values include mutations associatedwith hereditary spongiform endephalopathies, such as the A117V and V210Isubstitutions of the prion protein (Table 2). Predicted and experimentalvalues are in close agreement also for the A53T mutation associated withearly-onset Parkinson's disease and for various mutations associatedwith the amyloid β-peptide and responsible for either early-onsetAlzheimer's disease or hereditary cerebral hemorrhage with amyloidosis(Table 2).

If the analysis is repeated using only one single determinant tocalculate the ln(ν_(mut)/ν_(wt)) values, significant correlations werestill found between calculated and observed values of ln(ν_(mut)/ν_(wt))(p=0.0003 using only ΔHydr to calculate ln(ν_(mut)/ν_(wt)), p=0.036using only ΔΔG_(coil-α)+ΔΔG_(β-coil) and p=0.011 using only ΔCharge).Nevertheless, these correlations are less remarkable than that observedwhen considering a combination of all three factors and the slopes aresignificantly less than 1.0 (0.61, 0.19 and 0.10 using only ΔHydr, onlyΔΔG_(coil-α)+ΔΔG_(β-coil) and only ΔCharge, respectively). Thisdemonstrates that the equation in which these factors are combined givesa more accurate method for determining the ratio of rate of aggregationfor modified (e.g. mutant) and reference (e.g. wild type) polypeptides.

The correlation shown in FIG. 2( a) between theoretical and experimentaleffects of mutations on aggregation was found to be striking,considering the heterogeneous group of protein and peptide systems usedin the analysis as well as the variability of sites at which the variousmutations occur.

Example 4 Applicability of the Algorithm to Modifications InvolvingSeveral Amino Acid Residues and the Use of Kinetic Parameters Other than“Aggregation Rates”

Equation 1 was tested against other systems to evaluate itsapplicability to broader systems. Calculations used to derive Equation 1are based on the aggregation kinetics experienced by protein and peptidevariants that differ in a single residue from the original sequence. Therates (ν_(mut) and ν_(wt)) used in the expression correspond to theexponential phase of aggregation for each one of the peptides, and donot include any possible lag period or nucleation phase preceding thatstage.

To test the validity of this expression in predicting the aggregationpropensities of peptides derived from two Calcitonin variations wereincluded. The first was to evaluate if the effect of severalsubstitutions could be predicted in the same manner the algorithm wasable to do with single point mutations. The second was to include as akinetic parameter the relative ratio of aggregation times(τ_(mut)/τ_(wt)). By including the effect of a lag phase on the kineticsof aggregation exhibited by the peptides, the aggregation times for eachone of the peptides (τ), could be defined in two different ways: thefirst one was the nucleation time or time that precedes the initiationof aggregation or the development of turbidity in the solution (TI), andthe second one would correspond to the half time of aggregation or thetime at which variations in the measurements used for monitoringaggregation (light scattering, or any other method) reached half of itmaximum value (T2). This might enable the application of the equation tothe prediction of aggregation propensities for a much broader range ofmolecules with important design aspects.

The calculations were made on two variants of Calcitonin, using dataavailable in the literature (Arvinte, et al. 1993, J Biol Chem 268:6415-6422), and previous studies included in another patent applicationby some of the members of the group (Zurdo & Dobson, WO 02/083734,PCT/GB02/01778). The calculations were made using data disclosed inthose publications, producing the values indicated in table 3. In bothcases the value for the τ_(wt) parameter was obtained independently.

TABLE 3 Predicted and experimental changes in times of aggregationexhibited by various calcitonin peptides when compared to the humansequence. Calculated Observed Calculated Observed ln(ν_(mut)/ν_(wt))ln(ν_(mut)/ν_(wt)) (τ_(mut)/τ_(wt)) (τ_(mut)/τ_(wt)) ¹Salmon-1 −10.54−10.31 37,681.05 ~30,000^(a) ²SEQ ID NO 14 −5.60 −4.61^(b)/−5.71^(a)271.70 100^(b)/300^(a) ¹Data obtained from Arvinte et al. (1993) J BiolChem 268, 6415-6422. Salmon calcitonin has 16 modified positions whencompared to the human sequence. ²Sequence reported in Zurdo & Dobson (WO02/083734, PCT/GB02/01778), and Zurdo & Dobson (unpublishedobservations). Sequence ID NO 14 show 6 modified positions when comparedto the human sequence. ^(a)Values for calculating τ were obtained usingT1 as described above. ^(b)Values for calculating τ were obtained usingT2 as described above.

Calculations for changes in aggregations time were made assuming thefollowing relations with aggregation rates described by equation 1.

(τ_(mut)/τ_(wt))=(ν_(wt)/ν_(mut))=1/exp(ln(ν_(mut)/ν_(wt)))

This analysis shows that equation 1 can be used to predict theaggregation behaviour of a given polypeptide that has more than oneamino acid modification compared to the original polypeptide sequence.Moreover, it suggests that in systems where a lag phase is present, orthe aggregation rate can be difficult to calculate, alternative kineticparameters represented by the times of aggregation (either T1—nucleationtime—or T2—half time of aggregation—) can provide valid values tocompare with the predictions given by Equation 1.

Example 5 Applicability of the Algorithm to Modifications InvolvingAddition or Deletion of Amino Acid Residues: Aβ Peptides Linked withAlzheimer's Disease

Peptides Aβ(1-40) and Aβ(1-42) that are associated with Alzheimer'sdisease show differences in their aggregation propensities. The peptidesdiffer in sequence only by two residues at the C-terminus. The methodsof the invention explain the higher propensity to aggregate of the 42residues form, relative to the 40 residues form, of the amyloid βpeptide associated with Alzheimer's disease (Jarrett et al., 1993).Indeed, although the α-helical propensity and charge of the entirepeptide appear to be unchanged upon addition of the dipeptide Ile-Ala atthe C-terminus, the values of hydrophobicity and β-sheet propensity ofthe two residues are higher than the average values calculated over theentire peptide.

From a quantitative point of view, the change of hydrophobicityresulting from the addition of the two residues at the C-terminus can becalculated as ΔHydr=Hydr_(wt)−Hydr_(mut), where Hydr_(wt) is the averagehydrophobicity of the 40 residues forming the short form of the peptide;Hydr_(mut) is the average hydrophobicity of the two inserted residues(Ile-Ala). The change of β-sheet propensity resulting from insertion canbe calculated similarly. This leads to the prediction that the long formaggregates 7 times faster than the short form, in good agreement withthe kinetic profile reported by Jarrett et al., 1993 who foundacceleration of 7-8 times (Jarrett J T, Berger E P, Lansbury P T Jr. Thecarboxy terminus of the beta amyloid protein is critical for the seedingof amyloid formation: implications for the pathogenesis of Alzheimer'sdisease. Biochemistry, 32, 4693-4697 (1993)).

Example 6 Computer System for Operating the Method of the Invention

Referring now to FIG. 3, this shows a block diagram of a computer systemfor implementing an embodiment of the above-described method. A generalpurpose computer system 300 comprises a processor 300 a coupled toprogramme memory 300 b storing computer programme code to implementembodiments of the method, as described further below, and interfaces300 c such as conventional computer screen, keyboard, mouse, andprinter, as well as other interfaces such as a network interface, acontrol interface for a peptide synthesiser and software interfaces suchas a database interface.

The computer system 300 accepts user input from a input device 304 suchas a keyboard, input data file, or network interface, and provides anoutput to an output device 308 such as a printer, network interface, ordata storage device. Input device 304 receives an input comprising anamino acid sequence for the modified (e.g. mutant) peptide as well as pHand temperature values appropriate to an environment for which theaggregation rate of the polypeptide is determined. A glycine/prolinecorrection factor, such as a weight for a structural distortion factorinterfering with inter-molecular β-sheet formation or aggregation, mayalso be inputted. The output device 308 provides a comparativeaggregation rate information such as a log (base 10 or natural)aggregation ratio, for example, a ratio of half times for aggregation ofa mutant as compared with a wild type polypeptide.

Computer system 300 is coupled to a data store 302 which storeshydrophobicity data, β-sheet propensity data (either as propensity dataper se or in terms of free energy) and charge data. This data is storedfor each amino acid (residue) and preferably a plurality of sets of eachof these data types is stored corresponding to different values of pHand temperature. The computer system, in the illustrated embodiment, isshown interfacing with an α-helix propensity calculator 306. This may bea separate machine, for example, coupled to computer system 300 over anetwork, or may comprise a separate programme running on general purposecomputer system 300, or in other embodiments α-helix propensity code maybe stored within programme memory 300 b and operate in a unitary fashionwith the aggregation rate determination code described below. Howeverwhichever method is employed the α-helix propensity calculator receivessequence data, indirectly from the user input device, and providesα-helix propensity data in return. This data and the data in data store302 may either be determined on an amino acid by amino acid basis or maybe determined taking into account sequence context, for example, using awindow over the sequence to modify data values dependent uponneighbouring amino acids.

As illustrated, computer system 300 may also provide a data controloutput 310 to an automated peptide synthesiser 312. The control datawill generally comprise an amino acid sequence of a polypeptide. In thisway computer system 300 may be programmed to automatically compare theproperties of a number of modified (e.g. mutant) polypeptides and selectone or more of those which are predicted to have favourable propertiesfor automated synthesis. An example of such an automated peptidesynthesiser would be an ABI 433A Peptide Synthesiser (AppliedBiosystems).

Referring next to FIG. 4, this shows a procedure for determining acomparative aggregation rate along the lines described above. FIG. 4represents a flow diagram of an embodiment of code running in programmememory 300 b of FIG. 3.

At step S400 a user inputs an amino acid sequence, pH and temperaturedata, optionally with C- and N-terminus data for the sequence. Then atstep S402 the computer system reads hydrophobicity data for the inputsequence from the data store and sums this to provide an estimate ofhydrophobicity for the peptide coded by the sequence. Where, as isstrongly preferable, data for a range of pH and temperature values isavailable, data most closely corresponding to the desired pH andtemperature is retrieved. Then as steps S404 and S406, the procedurereads charge data and β-sheet propensity data from the data store in asimilar manner, summing the charge data to provide a charge estimate forthe polypeptide corresponding to the input sequence and, similarly,summing the β-sheet propensity data (normally expressed in terms of freeenergy). With proline, no β-sheet propensity value is available and so aproline residue may be skipped when summarising these values or anarbitrary β-sheet propensity value or one corresponding to another aminoacid may be employed. For example, if β-sheet propensity is expressed interms of free energy, an arbitrary value of 1, or a value correspondingto another amino acid can be used. Optionally steps S402 and S406 mayemploy a “window” (for example of 3, 5, 7, or more amino acids) thatwould include a correction for the effect of flanking residues on theproperties of a particular amino acid, (i.e. to take account of nearneighbours within an amino acid sequence), rather than considering eachamino acid of the sequence individually.

Step S408 the procedure provides the input sequence to an α-helixpropensity calculator, with the pH and temperature data, and, whereavailable, with the C- and N-terminus data. An α-helix propensitycalculator S408 a operates on this data and returns data back to theprocedure at step S410, the returned data comprising an α-helixpropensity value for the complete sequence. Suitable programme code forα-helix propensity calculator S408 a comprises the AGADIR code availablefromhttp://www.embl-heidelberg.de/Services/serrano/agadir/agadir-start.html,GOR4 code available fromhttp://npsa-pbil.ibcp.fr/cgi-bin/npsa_automat.pl?page=npsa_gor4.html andother codes described above. The skilled person will recognise that, ifdesired, this code or a newly designed code derived from publiclyaccessible (described in the scientific literature) or additionalexperimental data may be incorporated within the code implementing theprocedure of FIG. 4 rather than being implemented as a separateprocedure.

At step S412 the procedure then determines the comparative aggregationrate of the polypeptide defined by the input amino acid sequence ascompared with a reference polypeptide, using equation 1 above. It can beseen from equation 1 that a determination of comparative aggregationrate requires a difference in hydrophobicity, secondary structuralpropensity, and charge, and values for hydrophobicity, secondarystructural propensity and charge for the reference polypeptides mayeither be determined by repeating steps S400 to S410 for the referencepolypeptide or by reading stored values of these parameters from datastore 302, or in any other conventional manner. If desired at step S412the parameters or scaling factors in equation 1 operating on thedifferences in hydrophobicity, structural propensity and charge can beselected from sets of suitable parameters (step S414) in response toinput data such as polypeptide type data. For example, a completelyrandom coil polypeptide may use different parameters to a partiallyunfolded or structured polypeptide. Also, a polypeptide rich in aspecific type of residue, such as aromatic or charged amino acids, mayrequire different parameters.

After determining the comparative aggregation rate an optionalcorrection may be applied at step S416 for proline and or glycineresidues in order to account for additional conformational or structuralpreferences that may hinder formation of inter-molecular β-sheet oraggregated structures by a given polypeptide and then at step S418 thesystem outputs the result of the comparative aggregation ratecalculation. This may comprise a simple positive or negative valueindicating whether the aggregation rate of the modified polypeptide(e.g. mutant) is greater or less than that of the reference polypeptide,but preferably this comprises quantitative data relating to thecomparative aggregation rates such as a log aggregation rate ratio.

FIG. 5 shows a flow diagram of one advantageous implementation of theprocedure of FIG. 4. In particular FIG. 5 shows a method of screeningmodified polypeptides (e.g. mutations) in order to select candidateswith promising properties for further investigation and, optionally,synthesis. Thus at step S500 an amino acid sequence for a referencepolypeptide is input together with data identifying one or more modified(e.g. mutant) positions. Optionally the procedure may also allow amodification or range of modifications to be specified, for example interms of a pre-determined set or selection of amino acids.

Following initialisation, at step S502 the procedure generates amodified sequence representing one of the possible permutations definedby the input data and then, at step S504, determines a comparativeaggregation rate for modified polypeptide in comparison with thereference polypeptide, for example using the procedure at FIG. 4. Then,at step S506, the procedure checks whether there are any morepermutations for which to perform the calculation, and if so returns tostep S502 until a complete set of possible permutations has beengenerated. Then, at step S508, the set of comparative aggregation ratedata for each modified polypeptide (in comparison with the referenceprotein) is output, for example as an autolist, graph, or in any otherconvenient manner. This data may then be used, for example to identifycandidates for synthesis and/or for comparison with other data such asimmunogenicity/antigenicity. In particular, one or more of the ‘best’modified polypeptides, for example mutants with a particularly high orlow aggregation rate, may be collected and the sequence data for thesemodified polypeptides output to an automated peptide synthesiser such assynthesiser 312 of FIG. 3 to automatically produce the mutant proteinsfor, say, further investigation.

BIBLIOGRAPHY

-   Dobson, C. M. Protein folding and its links with human disease.    Biochem. Soc. Symp. 68, 1-26 (2001).-   Jarrett, J. T., Berger, E. P. & Lansbury, P. T. Jr. The carboxy    terminus of the beta amyloid protein is critical for the seeding of    amyloid formation: implications for the pathogenesis of Alzheimer's    disease. Biochemistry 32, 4693-4697.-   Selkoe, D. J. Alzheimer's disease: genes, proteins, and therapy.    Physiol. Rev. 81, 741-766 (2001).-   Siepen, J. A. & Westhead, D. R. The fibril_one on-line database:    Mutations, experimental conditions, and trends associated with    amyloid fibril formation. Protein Sci. 11, 1862-1866 (2002).-   Volles, M. J. & Lansbury, P. T. Jr. Vesicle permeabilization by    protofibrillar α-synuclein is sensitive to Parkinson's    disease-linked mutations and occurs by a pore-like mechanism.    Biochemistry, 41, 4595-4602 (2002).

For the following documents the numbers are those used in table 2:

-   11. Azriel, R. & Gazit, E. Analysis of the minimal amyloid-forming    fragment of the islet amyloid polypeptide. An experimental support    for the key role of the phenylalanine residue in amyloid    formation. J. Biol. Chem. 276, 34156-34161 (2001).-   12. Sakagashira, S., Hiddinga, H. J., Tateishi, K., Sanke, T.,    Hanabusa, T., Nanjo, K. & Eberhardt, N. L. S20G mutant amylin    exhibits increased in vitro amyloidogenicity and increased    intracellular cytotoxicity compared to wild-type amylin. Am. J.    Pathol. 157, 2101-2109 (2000).-   13. Salmona, M., Malesani, P., De Gioia, L., Gorla, S., Bruschi, M.,    Molinari, A., Della Vedova, F., Pedrotti, B., Marrari, M. A., Awan,    T., Bugiani, O., Forloni, G., Tagliavini, F. Molecular determinants    of the physicochemical properties of a critical prion protein region    comprising residues 106-126. Biochem. J. 342, 207-214 (1999).-   14. Thompson, A. J., Barnham, K. J., Norton, R. S., Barrow, C. J.    The Val-210-Ile pathogenic Creutzfeldt-Jakob disease mutation    increases both the helical and aggregation propensities of a    sequence corresponding to helix-3 of PrP(C). Biochim. Biophys. Acta.    1544, 242-254 (2001).-   15. Conway, K. A., Lee, S. J., Rochet, J. C., Ding, T. T.,    Williamson, R. E. & Lansbury, P. T. Jr. (2000). Acceleration of    oligomerization, not fibrillization, is a shared property of both    alpha-synuclein mutations linked to early-onset Parkinson's disease:    implications for pathogenesis and therapy. Proc. Natl. Acad. Sci.    USA, 97, 571-576.-   16. Giasson, B. I., Murray, I. V., Trojanowski, J. Q. & Lee, V. M. A    hydrophobic stretch of 12 amino acid residues in the middle of    α-synuclein is essential for filament assembly. J. Biol. Chem. 276,    2380-2386 (2001).-   17. Van Nostrand, W. E., Melchor, J. P., Cho, H. S.,    Greenberg, S. M. & Rebeck, G. W. (2001). Pathogenic effects of D23N    Iowa mutant amyloid beta-protein. J. Biol. Chem. 276, 32860-32866.-   18. Miravalle L, Tokuda T, Chiarle R, Giaccone G, Bugiani O,    Tagliavini F, Frangione B, Ghiso J. J Biol Chem 2000 Sep. 1;    275(35):27110-6-   19. Nilsberth, C., Westlind-Danielsson, A., Eckman, C. B.,    Condron, M. M., Axelman, K., Forsell, C., Stenh, C., Luthman, J.,    Teplow, D. B., Younkin, S. G., Naslund, J. & Lannfelt, L. (2001).    The ‘Arctic’ APP mutation (E693G) causes Alzheimer's disease by    enhanced Aβ protofibril formation. Nature Neurosci. 4, 887-893.-   20. Esler, W. P., Stimson, E. R., Ghilardi, J. R., Lu, Y. A.,    Felix, A. M., Vinters, H. V., Mantyh, P. W., Lee, J. P. &    Maggio, J. E. Point substitution in the central hydrophobic cluster    of a human β-amyloid congener disrupts peptide folding and abolishes    plaque competence. Biochemistry, 35, 13914-13921 (1996).-   21. Barghom, S., Zheng-Fischhofer, Q., Ackmann, M., Biernat, J., von    Bergen, M., Mandelkow, E. M. & Mandelkow, E. (2000). Structure,    microtubule interactions, and paired helical filament aggregation by    tau mutants of frontotemporal dementias. Biochemistry, 39,    11714-11721.-   22. Gamblin, T. C., King, M. B., Dawson, H., Vitek, M. P., Kuret, J.    Berry, R. W., Binder, L. I. In vitro polymerization of tau protein    monitored by laser light scattering: method and application to the    study of FTDP-17 mutants. Biochemistry, 39, 6136-6144 (2000).-   23. Nacharaju, P., Lewis, J., Easson, C., Yen, S., Hackett, J.,    Hutton, M. & Yen, S. H. Accelerated filament formation from tau    protein with specific FTDP-17 missense mutations. FEBS Lett. 447,    195-199 (1999).-   23b. Li, L., Von Bergen, M., Mandelkow, E. M. & Mandelkow, E.    Structure, stability, and aggregation of paired helical filaments    from tau protein and FTDP-17 mutants probed by tryptophan scanning    mutagenesis. J. Biol. Chem. in press (2002).-   24. Symmons, M. F., Buchanan, S. G., Clarke, D. T., Jones, G. &    Gay, N. J. X-ray diffraction and far-UV CD studies of filaments    formed by a leucine-rich repeat peptide: structural similarity to    the amyloid fibrils of prions and Alzheimer's disease β-protein.    FEBS Lett. 412, 397-403 (1997).-   25. Orpiszewski, J. & Benson, M. D. Induction of beta-sheet    structure in amyloidogenic peptides by neutralization of aspartate:    a model for amyloid nucleation. J. Mol. Biol. 289, 413-428 (1999).

All publications, patents, and patent documents are incorporated byreference herein, as though individually incorporated by reference. Theinvention has been described with reference to various specific andpreferred embodiments and techniques. However, it should be understoodthat many variations and modifications may be made while remainingwithin the spirit and scope of the invention.

1. A polypeptide synthesiser including computer program code to, whenrunning, select a polypeptide for synthesis, said code comprising codeto: create a set of candidate polypeptides from a reference polypeptidesequence; determine a relative rate of aggregation for each of saidcandidates; and select a said candidate for synthesis dependent upon theresults of said relative aggregation rate determining.
 2. A polypeptidesynthesiser as claimed in claim 1 wherein said a relative rate ofaggregation for each of said candidates comprises determining a relativeaggregation rate indicator for each of said candidates, said relativeaggregation rate indicator predicting a rate of aggregation of a saidcandidate polypeptide in comparison to a rate of aggregation of areference polypeptide specified by said reference polypeptide sequence,said candidate polypeptide comprising one or more amino acidmodification(s) when compared to the reference polypeptide, by:determining a difference in hydrophobicity between said candidatepolypeptide and said reference polypeptide; determining a difference ina secondary structure propensity between said candidate polypeptide andsaid reference polypeptide; determining a difference in charge betweensaid candidate polypeptide and said reference polypeptide; forming aweighted combination of said difference in hydrophobicity, saiddifference in secondary structure propensity, said difference in chargeto determine said relative aggregation rate indicator.
 3. A polypeptidesynthesiser as claimed in claim 2 wherein said weighted combinationcomprises a linear combination.
 4. A polypeptide synthesiser as claimedin claim 2 wherein said relative aggregation rate indicator comprises alogarithm of a ratio of aggregation rates of said second and referencepolypeptides.
 5. A polypeptide synthesiser as claimed in claim 2,further comprising determining weights for said weighted combinationusing known aggregation rates for mutations of said referencepolypeptide.
 6. A polypeptide synthesiser as claimed in claim 2 furthercomprising determining weights for said weighted combination using knownaggregation rates for mutations of a second reference polypeptide.
 7. Apolypeptide synthesiser as claimed in claim 2 wherein said secondarystructure propensity comprises a propensity to convert from an α-helicalto a β-sheet structure.
 8. A polypeptide synthesiser including acomputer system for determining a rate of aggregation of a secondpolypeptide in relation to a reference polypeptide, said secondpolypeptide and said reference polypeptide each having an amino acidsequence, the amino acid sequence of said second polypeptide comprisinga modified version of the amino acid sequence of said referencepolypeptide, the computer system comprising: a data store for storingdata comprising hydrophobicity data, β-sheet propensity data and chargedata for a set of amino acids; a program store storing processorimplementable code; and a processor, coupled to said program store andto said data store for implementing said stored code, the codecomprising code for controlling the processor to: input an amino acidsequence for said second polypeptide; read hydrophobicity data for saidsecond polypeptide amino acid sequence from said data store anddetermine a hydrophobicity value for said second polypeptide; readchange data for said second polypeptide amino acid sequence from saiddata store and determine a β-sheet propensity value for said secondpolypeptide; determine an α-helix propensity value for said secondpolypeptide; obtain hydrophobicity data, charge data, β-sheet propensitydata and an α-helix propensity value for said reference polypeptide; anddetermine said relative rate of aggregation using said hydrophobicity,change, β-sheet and α-helix propensity data for said second andreference polypeptides.
 9. A polypeptide synthesiser as claimed in claim8 wherein said code to determine said relative rate of aggregationcomprises code to determine an approximate value for a logarithm of aratio of an aggregation rate of said second polypeptide to anaggregation rate of said reference polypeptide.
 10. A polypeptidesynthesiser as claimed in claim 8 wherein said code to determine ahydrophobicity value for said second polypeptide is configured tocombine hydrophobicity values for amino acids of the sequence for thesecond polypeptide taking account of neighbours of an amino acid in thesaid sequence.
 11. A polypeptide synthesiser as claimed in claim 8wherein said code to determine a β-sheet propensity value for saidsecond polypeptide is configured to combine β-sheet propensity valuesfor amino acids of the sequence for the second polypeptide takingaccount of neighbours of an amino acid in the said sequence.
 12. Apolypeptide synthesiser as claimed in claim 8 wherein said code furthercomprises code to input a correction factor for Glycine and/or Proline,and wherein said code to determine said relative rate of aggregationfurther comprises code to apply said correction factor.
 13. Apolypeptide synthesiser as claimed in claim 8 wherein said data store isconfigured for storing said hydrophobicity data, β-sheet propensity dataand charge data for a plurality of temperatures and/or pH values,wherein said code further comprises code to input pH and/or temperaturedata for said second polypeptide, and wherein said code to read saidhydrophobicity data, β-sheet propensity data and charge data isconfigured to select data for reading from said data store dependentupon said pH and/or temperature input data.
 14. A polypeptidesynthesiser as claimed in claim 8 wherein said code to determine saidrelative rate of aggregation comprises code to evaluate xΔH+yΔG-zΔCwhere x, y and z are scaling factors, ΔH represents a difference inhydrophobicity between said second polypeptide and said referencepolypeptide, ΔG represents a difference between said second polypeptideand said reference polypeptide in propensity to convert from an α-helixstructure to a β-sheet structure, and ΔC represents a difference incharge between said second polypeptide and said reference polypeptide.15. A polypeptide synthesiser as claimed in claim 14 wherein said codefurther comprises code to input selection data, and code to select asaid scaling factor from said data store in response to said selectiondata.
 16. A polypeptide synthesiser as claimed in claim 8 wherein saidcode further comprises code to generate sequences for one or more secondpolypeptides, code to determine a said relative rate of aggregation ofeach of said one or more second polypeptide sequences, and code tooutput data corresponding to said determined relative rates ofaggregation.
 17. A polypeptide synthesiser as claimed in claim 8 whereinsaid code further comprises code to generate sequences for one or moreof said second polypeptides, code to determine a said relative rate ofaggregation of each of said one or more second polypeptide sequences,code for selecting a said generated sequence, and code to output saidselected sequences.
 18. A polypeptide synthesiser including computerprogram code to, when running, identify a modified polypeptide, the codecomprising: code to predict a change in aggregation rate for one or moremodified polypeptides, each modified polypeptide having one or moreamino acid modification(s) when compared to the reference polypeptide,the change in rate being a change from an aggregation rate of saidreference polypeptide; and code to identify one or more of said modifiedpolypeptides dependent upon said predicted change in aggregation rate.19. A polypeptide synthesiser as claimed in claim 18 wherein saidcomputer program code comprises code to, when running, predict theeffect of an amino acid modification on said rate of aggregation of asaid modified polypeptide, the code comprising code to: input an aminoacid modification that would convert said reference polypeptide to amodified form of the polypeptide; calculate a difference inhydrophobicity (ΔHydr) between the reference polypeptide and themodified polypeptide; calculate a difference in β-sheet propensity(ΔΔG_(coil-α)+ΔΔG_(β-coil)) between the polypeptide and modifiedpolypeptide; calculate a difference in charge (ΔCharge) between thepolypeptide and modified polypeptide; and calculate:[x*ΔHydr]+[y*(ΔΔG_(coil-α)+ΔΔG_(β-coil))]−[z*ΔCharge], wherein x, y andz are scaling factors.
 20. A polypeptide synthesiser as claimed in claim19 wherein a value for[x*ΔHydr]+[y*(ΔΔG_(coil-α)+ΔΔG_(β-coil))]−[z*ΔCharge] of a first signindicates that the modified polypeptide has a greater propensity toaggregate relative to the reference polypeptide and a value for[x*ΔHydr]+[y*(ΔΔG_(coil-α)+ΔΔG_(β-coil))]−[z*ΔCharge] of a sign oppositeto the first sign indicates that the modified polypeptide has a reducedpropensity to aggregate relative to the reference polypeptide.
 21. Amethod according to claim 19, wherein the effect of amino acidmodification on the rate of aggregation is expressed asln(ν_(mod)/ν_(ref)), wherein a positive value for ln(ν_(mod)/ν_(ref)),indicates that the modified polypeptide has a greater propensity toaggregate (lower solubility) relative to the reference polypeptide; anda negative value for ln(ν_(mod)/ν_(ref)), indicates that the modifiedpolypeptide has a reduced propensity to aggregate (higher solubility)relative to the reference polypeptide.
 22. A method according to claim19, wherein the scaling factor x is a value from 0.59 to 0.64 to, thescaling factor y is a value from 0.19 to 0.22 and the scaling factor zis a value from 0.49 to 0.51.
 23. A method according to claim 19,wherein x is 0.6, y is 0.2 and z is 0.5.
 24. A method according to claim19, wherein x is 0.63, y is 0.20 and z is 0.49.